Implement guidance

ABSTRACT

Efficient towed implement guidance to a desired path is achieved by guiding a towing vehicle toward a path on the opposite side of a desired path, then guiding the vehicle back to the desired path. Efficient forward implement guidance to a desired path is achieved by guiding a pushing vehicle along a tractrix. A vehicle leaves a straight line along a tractrix to keep a rear implement on the line as long as possible.

RELATED APPLICATIONS

This application is related to “Implement guidance”, U.S. Ser. No.14/293,739, filed on Jun. 2, 2014.

TECHNICAL FIELD

The disclosure is related to agricultural autopilots for vehicles thatpull or push farm implements.

BACKGROUND

Modern farm tractors, guided by autopilots, maneuver across farm fieldswith position accuracy and repeatability better than an inch. Automatic,precise vehicle control saves time and energy compared to sloppyoperating. It allows farmers to work more efficiently and spend lessmoney on fertilizers and pesticides. Consumers enjoy lower prices forhigh quality produce, and farm chemical waste and runoff are reduced.

One of a tractor's primary tasks is pulling implements such as disks,mulch rippers, chisel plows, air seeders, box drills, planters, and thelike, across fields in a uniform pattern of parallel lines. Theseoperations are often begun from an initial “A to B” (or simply “AB”)line. A set of lines parallel to the AB line defines how the tractorcovers a field. Before real work can begin, the tractor and whateverimplement it is pulling must both be established precisely on the ABline. Guiding a large implement onto a line efficiently is not as easyas it sounds for either a human operator or an autopilot.

Although an autopilot efficiently guides a tractor to a line, animplement towed behind takes a long time (and distance) to becomeestablished on the line within required tolerances. One technique thathas been tried to overcome this problem is to tune autopilot feedbackparameters such that the tractor tends to overshoot when joining adesired path. When the tractor overshoots, the implement arrives at thedesired path sooner. (An analogous maneuver is performed by atractor-trailer driver who intentionally overshoots a turn at a streetcorner. He drives the tractor to ensure that the trailer gets to itslane promptly rather than jumping the curb and only slowly approachingwhere it is supposed to go.)

Overshoot provoked by tuning feedback gains in an autopilot is noteasily controllable, however; there is no way to select an amount ofovershoot for instance. Furthermore, changing feedback gain to provokeovershoot can render the tractor unable to stay on its desired pathreliably. It also does not prevent undesirable actions such asjack-knifing; i.e. allowing the angle between tractor and implement tobecome too large.

Other implement guidance challenges include guiding forward, pushedimplements onto a line, and guiding rear implements along a line as longas possible as vehicle pulling them leaves a line.

What are needed are autopilots for farm tractors (or any kind ofvehicle) that guide the tractor so that towed implements, fixed rearimplements or fixed forward implements join or leave desired pathsefficiently, subject to constraints of good behavior such as notbreaking draw bars, implements, etc.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a tractor towing an implement, and a desired path.

FIG. 1B shows a tractor towing an implement on a desired path.

FIG. 2 shows a tractor, controlled by a feedback autopilot, towing animplement to a desired path.

FIG. 3A shows a tractor towing an implement, and various parametersassociated with modeling tractor and implement behavior.

FIG. 3B shows a tractor towing a chain of two implements.

FIG. 4 is a flow chart for a method of towing an implement onto adesired path with a vehicle controlled by a feedback autopilot.

FIG. 5 shows a tractor, controlled by a path-planning autopilot, towingan implement to a desired path.

FIGS. 6A and 6B illustrate tractor and implement paths for cases of noovershoot and too much overshoot, respectively.

FIGS. 7A and 7B illustrate tractor and implement paths for cases of toolittle and optimal overshoot, respectively.

FIG. 8 is a flow chart for a method of towing an implement onto adesired path with a vehicle controlled by a path-planning autopilot.

FIG. 9 is a block diagram of a path planning autopilot includingfeedback and feed-forward controllers.

FIG. 10 is a block diagram of a feedback control system based on pathplanning algorithms.

FIG. 11 is a block diagram of a feedback and feed-forward control systemin feedback mode.

FIG. 12 is a block diagram of a feedback and feed-forward control systemin combined feedback and feed-forward mode.

FIG. 13 illustrates tractor and implement paths when maximum permissibleovershoot is restricted.

FIG. 14 shows a tractor pushing an implement.

FIG. 15 shows a tractor pushing an implement to join a desired path.

FIG. 16 shows a tractor with a fixed, rear implement leaving a path.

FIG. 17 shows a tractor leaving a straight-line path while towing animplement.

DETAILED DESCRIPTION

Implement guidance systems and methods described below guide a vehiclesuch that an implement towed or pushed by the vehicle performs a desiredmaneuver, such as joining or leaving a desired path, efficiently.Normally the goal is to keep an implement on a desired path as much aspossible—joining a path as soon as possible, or staying on the path aslong as possible. The systems and methods ensure that constraints, suchas maximum allowed angle between vehicle and implement, maximum vehiclecurvature or maximum vehicle curvature rate, are obeyed. Usually theintended vehicle is a farm tractor and the implement is a farm implementsuch as a plow or seeder. However, implement guidance is also applicablein other scenarios involving construction vehicles, mining trucks, armytanks, etc. Hence, as used herein the word “tractor” or vehicle mayrefer to any vehicle that pushes or pulls an implement. In many of theexamples below a farm tractor with steerable front wheels is used forpurposes of illustration. However, the techniques described for anautopilot guiding a vehicle are equally applicable to vehicles with rearsteerable wheels, articulated vehicles or tracked vehicles.

In the case of towed implements, efficient implement guidance to adesired path is achieved by guiding a towing vehicle toward a path onthe opposite side of the desired path, then guiding the vehicle back tothe desired path. The desired path may be a straight line, a circle oran arbitrary curve. A path that is on the opposite side of the desiredpath from the vehicle's initial position is called an “offset path”. Theperpendicular distance between the desired path and the offset path iscalled the “offset” or “overshoot”. Implement guidance systems estimatea required offset, guide a vehicle toward the offset path, and guide thevehicle back to the desired path. The value of the offset or overshootis pre-determined for each maneuver.

In most cases the vehicle path only touches the offset path at onepoint. (In that case the offset path may contain only a single point orbe represented by an offset distance.) In some cases the vehicle neverreaches the offset path. In other cases, the vehicle may drive along theoffset path for a short distance in cases where the maximum vehicleovershoot from the desired path is restricted.

If an implement is steerable, then its implement steering may be used tokeep it on a path designed for a passive, non-steerable implement.Implement steering is generally capable of only small corrections,however. Normally implement steering is engaged only when an implementis already on or close to a desired path.

A vehicle or implement has “reached” a path (or is established “online”)when it remains within some fixed error distance from the path. (Avehicle or implement that merely crosses a path, but does not stay nearit is not online.) A vehicle may be said to have “reached” a path whenit stays within two centimeters of the path, as an example.

FIG. 1A shows a tractor 105 towing an implement 110, and a desired path115. The situation shown in FIG. 1A is a typical initial condition forimplement guidance: a tractor and implement are in an arbitrary positionand configuration. The position and configuration of the tractor may bedescribed by coordinates (x, y), heading (φ), and curvature (θ). Theconfiguration of the implement may be described by the position of itsattachment point to the tractor and its heading. FIG. 1B shows tractor105 towing implement 110 on desired path 115. The situation shown inFIG. 1B is the desired result of implement guidance: the tractor andimplement are both on the path; their heading is parallel to the path;and their curvature or steering angle is zero.

There are at least two broad classes of autopilot that may be used toguide a tractor and its implement onto a desired path: feedbackautopilots and path-planning autopilots. Feedback autopilots usefeedback control loops (e.g. a proportional-integral-derivative or “PID”controller) to minimize error signals. A feedback autopilot may bedesigned to minimize cross-track error (“XTE”) and heading error, forexample. (XTE is the distance from a vehicle to the nearest point on adesired path.) A path planning autopilot creates an efficient joiningpath that takes the vehicle from an arbitrary initial configuration (y,φ, θ) to a desired path. The initial configuration may be near or farfrom the desired path. After the joining path is created, the vehiclefollows it to the desired path.

Implement guidance techniques may be performed by either feedback orpath-planning autopilots. In the case of a feedback autopilot, theoverall procedure involves guiding the vehicle toward the offset path,the vehicle crossing the desired path, and guiding the vehicle back tothe desired path. As an example, FIG. 2 shows a tractor 205, controlledby a feedback autopilot, towing an implement 210 to a desired path,dotted line 215. Offset path 220 is represented by a dashed line. It isoffset from the desired path by offset “d”. Heavy solid line 225 showsthe path taken by tractor 205 under feedback autopilot control whilelight solid line 230 shows the path taken by implement 230 as it istowed by the tractor.

When a feedback autopilot guides a vehicle toward an offset path, theoffset is a predetermined constant. It is known before the vehiclereaches the path. Vehicle/implement simulations may be used to predictthe results of different offsets. An offset that is either too big ortoo small leads to an implement joining a desired path slower thannecessary. A simulation may be repeated with different offsets to findan optimal offset value. Simulations estimate vehicle and implementpaths based on: feedback autopilot inputs and characteristics (e.g. gainsettings), a vehicle model, and an implement model.

FIG. 3A shows a tractor 305 towing an implement 310, and parametersassociated with modeling tractor and implement behavior. In the figure,the wheelbase of the tractor is labeled “B”, the hitch length “H”, andthe implement length “L”. Tractor heading is denoted φ_(V) and implementheading is φ_(I). Heading angles are measured with respect to the{circumflex over (x)} direction. Given these parameter definitions, anexample of an implement model (where H=0) is:

${\frac{\mathbb{d}}{\mathbb{d}t}\phi_{I}} = {{- \frac{v}{L}}{\sin\left( {\phi_{I} - \phi_{V}} \right)}}$

Here V is vehicle speed. The equation may be used to predict implementheading and path traveled given a vehicle path. When H≠0, computersimulations may be used. A vehicle path may be predicted given feedbackautopilot gains and vehicle parameters such as maximum curvature andmaximum curvature rate.

Appropriate offsets may be estimated for each vehicle—implementcombination and these offsets may be stored in a memory accessible tothe autopilot. The offset that leads to an implement joining a desiredpath as soon as possible depends on factors including: hitch length H,implement length L, vehicle curvature and curvature rate, and initialstates of a towing vehicle (y, φ_(V), θ) and implement φ_(I). In theabsence of better information, a useful starting value for offset isapproximately 30% of L; i.e. any value between 25% and 35% of L.

On the way toward the offset path, the vehicle crosses the desired path.Upon reaching the offset path, the vehicle is guided back to the desiredpath. In most cases the vehicle only touches the offset path at onepoint. It does not drive along the offset path. (Exceptions to thisbehavior are discussed below in connection with situations where themaximum offset value is restricted.)

In an alternate embodiment a vehicle is guided across the desired pathas before, but the offset path is set far away so that the vehicle neverreaches it. In this case, the criteria for the vehicle to turn back tothe desired path is that the implement has reached the desired path;i.e. the implement is within a predetermined error distance from thedesired path and is predicted to stay within that distance. This savesthe work of estimating an optimal offset. (Predicting whether or not animplement stays within an error distance from a desired path afterinitially getting that close to it may also be skipped at the risk ofunpredictable results in some cases.)

One way to direct a feedback autopilot to an offset path, whether acomputed distance from the desired path or far away, is to add theamount of the offset to the autopilot's cross track error. For example,if a vehicle is 5 meters from a desired path, then the cross track erroris 5 meters. One way to set a 1 meter offset is to add 1 meter to theautopilot's cross track error.

Guidance methods for a vehicle towing a single implement are alsoapplicable to a vehicle towing a chain of implements such as illustratedin FIG. 3B which shows a tractor towing a chain of two implements. InFIG. 3B, tractor 315 tows implement 320 which in turn tows implement325. The tractor's wheelbase is “B” and its hitch length is “H₁”. Thelength and hitch length of implement 320 are “L₁” and “H₂”, and thelength of implement 325 is “L₂”, as shown in the figure.

A few different strategies may be used with chains of implements. Onestrategy is to plan a tractor path to affect the behavior of the firstimplement in a chain (e.g. 320) and let subsequent implement follow withno attempt to control them. A second strategy is to treat the controlpoint 330 of the first implement as the (control point of the) “vehicle”and to guide this “vehicle” such that the second or subsequent implementbehaves in a desired manner, such as joining a desired path as quicklyas possible. Depending on the strategy chosen, the first or second (orsubsequent) implement can be made to join a desired path at the sametime as the towing vehicle. A compromise strategy has the firstimplement joining a desired path too early and the second implementjoining too late.

FIG. 4 is a flow chart for a method of towing an implement onto adesired path with a vehicle controlled by a feedback autopilot. The flowchart summarizes techniques just described. In FIG. 4, step 405 is“guide vehicle toward offset path”. The offset path may be just onepoint or it may be represented by an offset distance from the desiredpath. Step 425 is “cross desired path”. This means that the vehiclecrosses the desired path so that the implement arrives at the desiredpath sooner than if the vehicle did not cross it. Step 430 is “guidevehicle back to desired path”. Once the implement has reached thedesired path, the vehicle must return to the desired path so that thedesired configuration (see FIG. 1B) can be achieved.

Steps 410, 415 and 420 are options pertaining to guiding the vehicletoward the offset path. These steps are not all performed together. Step410 represents the option that the offset is a predetermined amountobtained from a stored valued in memory, from trying different offsetamounts in simulation, or from a rule of thumb such as 30% of L, asexamples. Alternatively, step 415 represents the option that the offsetis set far away from the desired path; in other words it is farther awayfrom the desired path than the vehicle needs to go to bring theimplement online in minimum time. Finally, step 420 represents theoption that the effect of an offset path is created by adding an offsetto the cross track error in a vehicle's feedback autopilot.

Steps 435 and 440 are “predict performance with models” and “compute newoffset”. Predicting performance means simulating vehicle and implementpaths given initial conditions, vehicle and implement characteristics,and offset values. Offset values may be computed based on simulationresults with previous offsets. For most initial conditions, if animplement becomes established online before the vehicle, then the offsetis too big; if the vehicle arrives online first, then the offset is toosmall.

Implement guidance may also be performed with a path planning autopilot.Unlike conventional autopilots, a path planning autopilot offers directcontrol over constraints such as maximum permitted steering angle ormaximum steering angle rate. Such constraints may be specified asfunctions of vehicle speed. Path planning techniques may be implementedas a complementary feed-forward capability of a feedback autopilot orthey may replace feedback all together.

Several kinds of path planning autopilots exist. An advanced pathplanning autopilot accepts heading, curvature and curvature rateconstraints. Such an autopilot is described in “Path planningautopilot”, U.S. patent application Ser. No. 13/470,028, filed on May11, 2012 and incorporated herein by reference. A more limited pathplanning autopilot (which may also be viewed as a special case of theadvanced path planning autopilot) cannot account for curvature rateconstraints. This kind of autopilot plans paths that include straightlines and circular arcs, but not clothoid segments. Such an autopilotdoes not guide a vehicle as smoothly as one that obeys curvature rateconstraints, but it may be adequate for slow speed maneuvers. A stillmore limited system is one that lays out an objective or series ofobjectives, other than the vehicle desired path, for a feedbackautopilot.

When a path planning autopilot performs implement guidance it computes afirst optimal vehicle path from an initial condition to an offset path.It then computes a second optimal path to join a desired path from theoffset path. (If the offset path is close to the desired path, however,path planning from the offset path back to the desired path may not benecessary; feedback may be sufficient.)

The first optimal path starts from the vehicle's initial condition whichis specified by its perpendicular distance, y, from the desired path,its heading, φ, and its curvature, θ. The first optimal path ends at theoffset path with (y, φ, θ)=(−d, 0, θ_(M)). Here, d is the amount ofoffset and θ_(M) is a specified curvature upon reaching the offset path.At the offset path y=−d because the offset path is on the opposite sideof the desired path from the vehicle's initial position. The secondoptimal path starts from (−d, 0, θ_(M)) and ends on the desired pathwith (y, φ, θ)=(0, 0, 0).

Both the first and second optimal paths obey curvature (θ) constraints.The paths also obey curvature rate (dθ/dt) constraints if the pathplanning autopilot is capable of taking them into account. Furthermore,the optimal paths obey implement constraints such as maximum implementangle, |φ_(I)−φ_(V)|, maximum implement curvature and maximum implementcurvature rate. (“Optimal” paths are optimal in theory and efficient inpractice.)

FIG. 5 shows a tractor 505, controlled by a path-planning autopilot,towing an implement 510 to a desired path 515 represented by a dashedline. Offset path 520 is represented by a dash-dot line and is separatedfrom the desired path by offset, d. The optimal path estimated by thepath planning autopilot and followed by the tractor is composed of twoparts: a first optimal path 525 from the tractor's initial position tothe offset path and a second optimal path 530 from the offset path tothe desired path. Vertical line 540 marks the boundary between lines 525and 530. The path followed by implement 510 is drawn as line 535. WhileFIG. 5 is a conceptual sketch, FIGS. 6 and 7, described below, areresults of path planning simulations.

Turning now to details of path planning for implement guidance, thefirst step is choosing an offset amount, d. In the absence of otherinformation a good first guess for the offset is 30% of L, the implementlength. Next, the curvature, θ_(M), needed at the offset path isestimated. This can be done analytically (e.g. using the methods of U.S.Ser. No. 13/470,028) or by lookup table. If θ_(M) is too large, thevehicle will overshoot the desired path when returning from the offsetpath. If θ_(M) is too small, the vehicle will join the desired pathslower than necessary. Once θ_(M) is chosen, an optimal path is plannedfrom the vehicle's present condition (y, φ, θ) to the offset path (−d,0, θ_(M)). Finally, an optimal path is planned from the offset path tothe desired path (0, 0, 0). These steps are repeated with differentoffsets until an offset is found that minimizes the distance required tobring the implement online. (This distance may be the total distancetravelled by the vehicle or implement, or an along-track distanceparallel to the desired path.) A binary search may be used to find thebest offset.

In most cases the best offset is the one that results in the vehicle andimplement arriving online at the same time. If the implement arrivesfirst, the offset is too big; if the vehicle arrives first, the offsetis too small. Exceptions can occur for unusual initial conditions suchas vehicle and implement on opposite sides of the desired path.

Path planning implement guidance results vary depending upon initialvehicle and implement conditions. An implement model may be used topredict implement behavior, but the model needs initial conditions forthe implement as input. There are several possible ways to estimate theinitial condition of the implement without any direct sensor forimplement position. One way is to assume that the implement trailsstraight behind the vehicle; i.e. φ_(I), =φ_(V). Although thisassumption may not be correct, it can still lead to useful results aspath planning solutions tend to converge as paths become longer. Asecond way is to assume an implement heading based on the tractor'ssteering angle. A third way to estimate the implement's condition isbased on vehicle history (the path it has taken in the recent past) andan implement model. Finally, if GPS, inertial, or mechanical sensors areavailable, then these may be used to estimate implement position and/orheading.

Once a vehicle path has been computed that brings the implement onlineas fast as possible, the path is checked to make sure it does not causethe implement to violate implement constraints. (By design the path doesnot violate vehicle constraints.) For example the implement may berestricted to maximum curvature or the angle between the implement andthe vehicle |φ_(I)−φ_(V)| may be restricted to a maximum value toprevent jack-knifing. If implement constraints are violated, thenmaximum vehicle curvature and/or maximum vehicle curvature rate may bereduced and all paths recomputed with new vehicle constraints.

As a final check, implement performance may be compared for a vehiclepath using a computed offset and a vehicle path using zero offset. Incertain special cases, e.g. vehicle and implement on opposite sides ofdesired path, the latter may prove to bring the implement online faster.If that is the case, then the zero offset solution is used.

FIGS. 6A, 6B, 7A and 7B show computed vehicle (heavy line) and implement(light line) paths for various offsets (i.e. “overshoot”). In each casethe initial vehicle condition is (5 m, 0, 0), H=1 m, and L=5 m. Thedesired path is the dotted line, y=0. The offset path is drawn as adot-dash line.

FIGS. 6A and 6B illustrate tractor and implement paths for cases of noovershoot and too much overshoot, respectively. In FIG. 6, lines 605 and615 are tractor paths while lines 610 and 620 are correspondingimplement paths. Line 625 is an offset path where the offset is 5 m.

FIGS. 7A and 7B illustrate tractor and implement paths for cases of toolittle and optimal overshoot, respectively. In FIG. 7, lines 705 and 720are tractor paths while lines 710 and 725 are corresponding implementpaths. Lines 715 and 730 are offset paths where the offset is 0.5 m and1.6 m, respectively.

Inspection of the figures reveals that the implement joins the desiredpath (y=0) soonest when the offset is 1.6 m. In this case the implementis online by approximately x=8 m. In all the other cases, the implementjoins the desired path later. In particular, the implement does not jointhe desired path until some point after x=14 in the “no overshoot” caseof FIG. 6A.

FIG. 8 is a flow chart for a method of towing an implement onto adesired path with a vehicle controlled by a path-planning autopilot. Theflow chart summarizes techniques just described. In FIG. 8, step 805 ischoose offset amount; step 810 is compute path(s); and step 830 ispredict implement performance. Based on the results of step 830, thethree steps are repeated until the implement joins the desired pathefficiently.

Details of computing paths are summarized by steps 815 (compute pathfrom initial vehicle position to offset path), 820 (compute path fromoffset path to desired path) and 825 (obey vehicle constraints). Notethat step 820 need not be performed if the offset path is close to thedesired path and feedback, rather than path planning, is used to guidethe vehicle from the offset path back to the desired path. Step 835(adjust performance limits) refers to checking that implementconstraints are not violated, and if they are, adjusting vehicleconstraints to avoid exceeding implement limits. Implement constraintsmay include an implement never exceeding a specified maximum angle withrespect to the vehicle, an implement never exceeding a specified maximumcurvature, and/or an implement never exceeding a specified maximumcurvature rate.

Examples of path planning autopilots capable of performing the steps ofFIG. 8 were described in U.S. Ser. No. 13/470,028 and are reviewed here.Path-planning implement guidance procedures may be executed byautopilots such as these.

FIG. 9 is a block diagram of a path planning autopilot includingfeedback and feed-forward controllers. The autopilot includes a mainunit 905 having a feedback controller, a feed-forward controller, aprocessor and memory. Functional blocks of the main unit may beimplemented with general purpose microprocessors, application-specificintegrated circuits, or a combination of the two.

The main unit receives input from GNSS (global navigational satellitesystem) receiver 910 and sensors 915. The main unit sends output toactuators 920. GNSS receiver 910 may use signals from any combination ofGlobal Positioning System, Glonass, Beidou/Compass or similar satelliteconstellations. The receiver may use differential corrections providedby the Wide Area Augmentation System and/or real-time kinematicpositioning techniques to improve accuracy. The receiver provides themain unit with regular position, velocity and time updates.

Sensors 915 include steering sensors that report vehicle steering angleand heading sensors that report vehicle heading to the main unit.Heading may be sensed from a combination of GNSS and inertialmeasurements. Steering angle may be sensed by a mechanical sensor placedon a steering linkage or by inertial measurements of a steering linkage.Sensors 915 may also be omitted if heading and curvature of vehicletrack are estimated from GNSS measurements alone.

Actuators 920 include a steering actuator to steer a vehicle. A steeringactuator may turn a vehicle's steering wheel or tiller, or it maycontrol a steering mechanism directly. On some vehicles steeringactuators operate hydraulic valves to control steering linkages withoutmoving the operator's steering wheel.

A path planning autopilot may include many other functions, sensors andactuators. For simplicity, only some of those pertinent to path planningoperations have been included in FIG. 9. A display and user inputdevices are examples of components omitted from FIG. 9. User input maybe necessary for system tuning, for example. The system of FIG. 9 mayoperate in different modes, three of which are illustrated in FIGS. 10,11 and 12.

A path planning autopilot may use path planning techniques in a feedbackcontrol system or it may use path planning in a combinedfeedback/feed-forward control system. FIG. 10 is a block diagram of afeedback control system based on path planning algorithms. In FIG. 10,feedback controller 1005 controls vehicle 1010 by sending curvature rate(u) or curvature (θ) command signals to it. Actual vehicle heading (φ)and cross track error (y) as measured by a GNSS receiver, heading sensorand/or other sensors are combined with desired curvature, heading andtrack (θ, φ, y) to form an error signal for controller 1005.

FIGS. 11 and 12 are block diagrams of a feedback and feed-forwardcontrol system in feedback, and combined feedback and feed-forwardmodes, respectively. In FIGS. 11 and 12, feedback controller 1105controls vehicle 1110 by sending curvature (θ) commands to it.(Alternatively, feedback controller 1105 may send curvature rate (u)commands to the vehicle.) Actual vehicle heading (φ) and cross trackerror (y) as measured by a GNSS receiver, heading sensor and/or othersensors are combined with parameters of a desired path 1120 to form anerror signal for controller 1105. Feedback controller 1105 may be aconventional PID controller unlike feedback controller 1005.

In FIGS. 11 and 12, solid arrows represent active signal paths, whiledashed arrows represent signal paths that are turned off. Thus in FIG.11, feedback controller uses an error signal derived from the differencebetween measured and desired paths to generate feedback control signalθ_(FB). This mode may be used when the vehicle is close to the desiredpath.

When the vehicle is far from a desired path, the control system switchesto the mode illustrated in FIG. 12. A typical scenario in which avehicle is far from a desired path is when an autopilot system isengaged before the vehicle is established on the path. A set of parallelswaths may have been created to guide a tractor over a farm field, forexample, and the tractor operator may want the autopilot to guide thetractor to the nearest one. When this happens, path joining planner 1115calculates an efficient path from the vehicle's present position to thedesired path.

Path joining planner 1115 calculates a joining path to guide the vehicleto the desired path and provides a feed-forward control signal, OFF,which is combined with feedback control signal θ_(FB) to guide vehicle1110. For purposes of feedback controller 1105, the joining path is thedesired path until the original desired path 1120 is reached. Thusfeedback reference signal (φ, y) is derived from the path joiningplanner during that time. The path joining planner is the feed-forwardmechanism described in connection with FIG. 9.

Alternatively, once path joining planner 1115 calculates a joining path,that joining path continuing onto the original desired path (from thepoint where the joining path meets the original path) may become the newdesired path. The original desired path before the point where thejoining path meets it may then be discarded.

Autopilots having a path-planning, feedback and feed-forward controlsystem like that of FIGS. 11 and 12 may use a switch to alternatebetween modes. The mode is selected based on vehicle distance fromdesired path 1120; near the path feedback control is used, far from itcombined feed-forward and feedback control is used. Criteria todetermine “near” and “far” may be based on characteristic lengths suchas vehicle wheelbase or distance travelled in a characteristic responsetime, or whether or not steering angle or steering angle rate limits areencountered.

Alternatively, a control system may operate in the mode illustrated inFIG. 12 continuously. When the vehicle is near the desired (1120) path,output signals from the path joining planner are small and may havenegligible practical influence on the feedback control system. Thus, thepath joining planner may be kept online all the time.

FIGS. 10-12 show measured (φ, y) data being combined with desired pathdata and then sent to feedback controller 1005 or 1105. However,measured data could alternatively be estimated by an observer, e.g. aKalman filter, before being combined with desired path data.

In addition to basic implement guidance, feedback or path-planningautopilots may be configured for advanced implement guidance procedures.FIG. 13 illustrates tractor and implement paths in an example wheremaximum permissible overshoot is restricted. Restrictions of maximumovershoot typically occur when a tractor must be prevented from drivingover, and potentially crushing, a crop row adjacent to the desired path.When maximum overshoot is restricted, a towing vehicle stays on anoffset path for a finite distance rather than merely touching the offsetpath at one point.

In FIG. 13, vehicle path V₁ produces implement path I₁, while vehiclepath V₂ produces implement path I₂. Offset D is the offset associatedwith vehicle path V₁ and it results in an implement joining desired path1305 as soon as possible. Restricted offset D_(L) is the offsetassociated with vehicle path V₂ which results in an implement joiningdesired path 1305 as soon as possible given the maximum-offsetconstraint.

A strategy for designing offset-constrained paths such as path V₂ is asfollows: If the implement undershoots the desired path even when thevehicle overshoots the desired path by the maximum permissible amount,then the distance travelled by the vehicle along the offset path isincreased by an increment and the system is simulated again. The optimumdistance for the vehicle to travel along the offset path is the one thatleads to the implement and the vehicle arriving on the desired path atthe same time. If the vehicle arrives on the desired path first, thenthe vehicle should stay on the offset path longer. On the other hand, ifthe implement arrives on the desired path first, then the vehicle shouldtravel on the offset path for a shorter distance. The optimal distancefor the vehicle to stay on the offset path may be estimated byiteration.

Another advanced situation occurs when operating on sloping terrain suchas a side slope. When a slope is detected or anticipated, all paths maybe adjusted uphill to compensate. “Agricultural autopilot pathadjustment”, U.S. Pat. No. 8,494,726 to Peake et al., issued on Jul. 23,2013, and incorporated herein by reference, provides techniques forestimating the amount of uphill adjustment needed. Implement slope maybe anticipated from a terrain map stored in a memory or from vehicleslope as sensed onboard a vehicle.

There are other possible methods to solve the implement guidanceproblem. As examples, solutions, that although not optimal may still beuseful, are now discussed. The first alternate method proceeds asfollows: First an optimal vehicle path is computed from the implement'sposition to the desired path. This optimal vehicle path now becomes theimplement path. A new vehicle path is computed based on the implementpath using geometric relationships between the vehicle and theimplement. (See for example techniques discussed in U.S. Pat. No.8,494,726.)

One drawback of this method is that the new vehicle path will violateconstraints used in computation of the original optimal vehicle path.For example, the curvature may become greater than allowed. A solutionto this is to make the original vehicle constraints more restrictive;e.g. reduce the maximum allowable vehicle curvature. Finally, thevehicle is guided along the new vehicle path.

A second alternate method proceeds as follows: First an optimal vehiclepath is computed for the vehicle to join the desired path. Next animplement model is used to predict the implement's path. The implement'soffset from the desired path at the point when the vehicle reaches thedesired path is noted, and then the vehicle path is displaced toward thedesired path by the amount of implement offset. The vehicle is thenguided along the displaced vehicle path. When the implement reaches thedesired path, feedback may be used to guide the vehicle from itsdisplaced position back to the desired path.

A third alternate method is to compute a spline (b-spline, cubic spline,etc.) path from the vehicle's initial position to a desired path. Asimulation of vehicle and implement behavior for the vehicle followingthe spline and the implement towed behind may be performed with the aidof vehicle and implement models. Spline parameters may then be adjustediteratively to find a spline that brings the vehicle and the towedimplement online simultaneously or nearly so.

Pushed implements also benefit from vehicle maneuvers; FIG. 14 shows atractor pushing an implement. In FIG. 14, tractor 1405 pushes a fixedimplement 1410. The implement is ahead of the tractor's control point(the center of the rear axle) by a distance F. (The control point of theimplement is marked with a target symbol on the implement.) An exemplarysituation is a harvester with a header fixed in front of it. Here theproblem is again how to maneuver the vehicle (e.g. tractor, harvester)so that the implement arrives on a desired path as quickly as possible.And similarly to the towed implement case, it is desirable to preventthe pushed implement from going past a desired path by more than somemaximum amount. Unlike a towed implement, a pushed implement is fixed;in other words it always has the same heading as the vehicle. FIG. 14shows F greater than the vehicle's wheelbase, B. However, situations inwhich F=B or F<B are not uncommon.

The basic strategy for establishing a pushed implement (or “forwardimplement”) on a desired path is: first, approach the path at less thanor equal to a maximum permissible approach angle; next, starting fromthe point where the implement first reaches the desired path, guide thevehicle along a tractrix; finally, resume normal vehicle guidance oncethe vehicle is established on the desired path.

A tractrix is a curve that solves the differential equation,

$\frac{\mathbb{d}y}{\mathbb{d}x} = {- \frac{\sqrt{a^{2} - x^{2}}}{x}}$

with initial condition y(a)=0.

The solution is,

$y = {{\int_{x}^{a}{\frac{\sqrt{a^{2} - t^{2}}}{t}{\mathbb{d}t}}} = {\pm \left( {{a\;\ln\;\frac{a + \sqrt{a^{2} - x^{2}}}{x}} - \sqrt{a^{2} - x^{2}}} \right)}}$

The first term of the solution may also be written α sech

$\,^{- 1}\left( \frac{x}{a} \right)$and other approximations to the tractrix may be feasible depending onspecific situations. Thus “tractrix” as used here refers both to theexact solution of the differential equation presented above and also toreasonable approximations to that solution such as hyperbolic functionsthat approach an axis asymptotically.

FIG. 15 shows a vehicle 1405 pushing implement 1410 to join desired path1420. The path taken by the vehicle is tractrix 1415. The control pointof the vehicle, at the center of the rear axle, is the point wherevehicle curvature, θ, and heading, φ, are computed. Note that in FIG.15, x and y are switched compared to the equations given above tomaintain consistency with earlier figures such as FIGS. 6 and 7. Usingthe equations, a=4 in FIG. 15, and the positive branch of the solutionis shown.

From the moment that the implement arrives at the desired path, theimplement path is a straight line along the desired path while the pathof the vehicle control point, at the center of the vehicle's rear axle,is along the tractrix. The shape of the tractrix is such that a=F, theimplement distance ahead of the control point.

If the vehicle were to approach the desired path at right angles, theimplement would first arrive at the desired path when the vehicle'scontrol point was F away from it. A tractrix with a=F provides thecorrect path for the vehicle to follow in this case. However, few actualvehicles can follow the tractrix from that initial condition because aninstantaneous change in steering angle from zero to 90 degrees isneeded.

A more reasonable solution is to specify a maximum acceptable approachangle. The vehicle shown in FIG. 15, for example, is angledapproximately 45 degrees to the desired path. An advanced autopilot canplan a path from an arbitrary initial vehicle condition to a conditionwhere the vehicle approaches at the desired path at a specified angle,φ_(M). The required vehicle curvature upon the implement reaching thedesired path is determined by the tractrix. Thus the autopilot plans apath from an arbitrary initial condition to one in which the curvatureand heading are (θ=f(φ_(M)), φ=φ_(M)). Here f(φ_(M)) expresses the ideathat a desired heading specifies a point on the tractrix, which in turnhas a computable curvature.

A more limited autopilot may not take curvature rate constraints intoaccount. In this case, a path may be planned from an arbitrary initialcondition to a straight line approach to a desired path at a desiredangle. When the implement reaches the desired path, the vehiclecurvature is changed to the curvature required by the tractrix asquickly as possible. This method may be adequate depending on vehiclespeed and selected approach angle. At slow speeds and shallow angles,the change in curvature may be small enough that any error introduced bynon-instantaneous curvature change is acceptable.

With either advanced or limited path-planning autopilots, following atractrix from an implement's point of initial contact with a desiredpath until the vehicle is established on the path provides a reliablemethod for establishing a front implement on a path without crossing thepath and possibly damaging adjacent crop rows. Mathematically thetractrix approaches the desired path asymptotically but never touchesit. Hence, “established” has the same sense here as “reached” or“online” mentioned earlier: the vehicle remains within some fixed errordistance from the path. The required tractrix is parameterized by theimplement length, F, ahead of the vehicle control point.

A tractrix also provides a useful vehicle path when departing from astraight line. For example, a tractrix provides a vehicle path thatkeeps a fixed, rear implement on a line as long as possible. FIG. 16shows a tractor 1605 with a fixed, rear implement 1610 leaving astraight-line path 1620. A fixed, rear implement is one that extendsfrom the rear of the vehicle, but always maintains the same heading, φ,as the vehicle. A fixed, rear implement is normally connected to avehicle via a three-point hitch.

When tractor 1605 follows tractrix 1615, implement 1610 remains on line1620 as long as possible. If the tractor follows the tractrix, theimplement will stay on the line until the tractor's heading is parallelto the y-axis. After that point, the implement will depart the line. Inpractice, the tractor cannot follow the tractrix that far as it runsinto practical steering angle and steering angle rate limits. Thus, inpractice, the implement leaves the line before it has turned 90 degrees.Following a tractrix as long as practical, however, keeps the implementon line longer and keeps the implement from going on the opposite sideof the line from the tractor and possibly damaging adjacent crop rows,for example. Whenever a path planning autopilot is available, therefore,a tractrix provides a useful path for a vehicle departing a line with arear, fixed implement such as often happens when initiating end-of-rowturns in agricultural operations. The tractrix in this case isparameterized by the fixed implement length, R, as shown in FIG. 16.

As a second example, a tractrix provides a vehicle path that keeps atowed, rear implement on a line as long as possible. FIG. 17 shows atractor 1705 leaving a straight-line path 1720 while towing an implement1710. When tractor 1705 follows tractrix 1715, hitch point 1712, andtherefore implement 1710, remain on line 1720 as long as possible. Ifthe tractor follows the tractrix, the hitch will stay on the line untilthe tractor's heading is parallel to the y-axis. After that point, thehitch point and implement will depart the line. In practice, the tractorcannot follow the tractrix that far as it runs into practical steeringangle and steering angle rate limits. Thus, in practice, the hitch pointleaves the line before the tractor has turned 90 degrees. Following atractrix as long as practical, however, keeps the hitch point andimplement on line longer and keeps the implement from going on theopposite side of the line from the tractor and possibly damagingadjacent crop rows, for example. Whenever a path planning autopilot isavailable, therefore, a tractrix provides a useful path for a vehicledeparting a line while towing an implement such as often happens wheninitiating end-of-row turns in agricultural operations. The tractrix inthis case is parameterized by the hitch length, H, as shown in FIG. 17.

In each of the maneuvers involving a tractrix, an autopilot guides avehicle along a tractrix parameterized by a characteristic of animplement attached to the vehicle. The characteristic of the implementmay be distance of the implement ahead of the vehicle's control point,implement length or hitch length, as examples.

Systems and methods for implement guidance have been described for towedand pushed implements. In the case of towed implements, efficientimplement guidance to a desired path is achieved by guiding a towingvehicle toward a path on the opposite side of the desired path, thenguiding the vehicle back to the desired path. In the case of pushedimplements, a tractrix parameterized by implement geometry provides asuitable vehicle path. In both cases, vehicle guidance is customized tofit the requirements of a specific implement. A vehicle may also followa tractrix when leaving a straight line path to keep a fixed or towedimplement on the line as long as possible.

The systems and methods described above may be applied in a wide varietyof agricultural and other situations. As an example, joining a straightpath is a part of turning a vehicle and implement around at the end ofone field row to join another row. All of the systems and methodsdescribed above may be implemented with the aid of modern microprocessortechnology, and as such, can generate vehicle commands “on-the-fly”.However, the case of turning around at the end of a field row is anexample where a desired maneuver can be anticipated well in advance. Insuch cases, vehicle autopilots may use stored or pre-computed algorithmsor vehicle paths instead of computing anew each time.

The above description of the disclosed embodiments is provided to enableany person skilled in the art to make or use the invention. Variousmodifications to these embodiments will be readily apparent to thoseskilled in the art, and the principles defined herein may be applied toother embodiments without departing from the scope of the disclosure.Thus, the disclosure is not intended to be limited to the embodimentsshown herein but is to be accorded the widest scope consistent with theprinciples and novel features disclosed herein.

What is claimed is:
 1. A method for guiding an implement along adesired, straight-line path comprising: a path-planning autopilotguiding a vehicle pulling the implement, the autopilot first guiding thevehicle along the desired, straight-line path; and, the autopilot thenguiding the vehicle away from the desired, straight-line path along atractrix such that the implement remains on the desired, straight-linepath.
 2. The method of claim 1, the implement being a fixed, rearimplement and the tractrix parameterized by implement length.
 3. Themethod of claim 1, the implement being a towed implement towed from ahitch on the vehicle and the tractrix parameterized by hitch length. 4.A vehicle autopilot comprising: a microprocessor and memory; a GNSSreceiver the provides vehicle position, velocity and time estimates tothe microprocessor; a feedback controller and a feed-forward controllerthat generate vehicle curvature commands to guide the vehicle; and, avehicle steering actuator; wherein, the autopilot guides the vehiclealong a tractrix parameterized by a characteristic of an implementattached to the vehicle.
 5. The autopilot of claim 4, the implementbeing a fixed, rear implement and the tractrix parameterized byimplement length.
 6. The autopilot of claim 4, being a towed implementtowed from a hitch on the vehicle and the tractrix parameterized byhitch length.